Lesson Two runners run on a quarter-mile oval track
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<H2>Two runners run on a quarter-mile oval track</H2> <H3>Problem 1</H3>Two long distance runners start from the same point simultaneously on a quarter-mile oval track and run in the same direction. Alex runs at a constant speed of exacly 10.98 mph, and Kelly runs at a constant speed of exacly 10.65 mph. How many feet will they be away from the starting point when Alex laps Kelly the SECOND time ? <B>Solution</B> <pre> Alex will laps Kelly <U>first time</U> at the moment, when Alex covers the distance, which exactly one quarter mile (precisely the length of the track) longer than the distance Kelly covers to this moment. ===--->>> It is <U>the key point</U> to understand when solving such problems (!) <<<---=== This condition takes the form of <U>THIS equation</U> 10.98*t - 10.65*t = 0.25, or (10.98 - 10.65)*t = 0.25, 0.33*t = 0.25 t = {{{0.25/0.33}}} = 0.757576 of an hour. At that time moment Kelly will cover 10.65*0.757576 = 8.068 miles. So, Kelly will complete 8*4 = 32 full quarter-mile track lengths and will be at 0.068 miles from the starting point on the track. To find the moment of the SECOND lap, we can formally determine the time when Alex will overtake/lap Kelly in two track lengths. It leads to the similar equation, but you can complete the solution even without using equation. Simply note that the position of the first lap now plays the role of the former starting point. As soon as you understand it, you will guess the <U>ANSWER</U>: ===--->>> the second lap point is remoted 2*0.068 = 0.136 miles from the starting point. <<<---=== </pre> My answer 0.136 of a mile means 0.136 of a mile counting in the same direction on the track as they run. 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